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Conformal invariance for nonholonomic system of Chetaev's type with variable mass

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Applied Mathematics and Mechanics(English Edition) 2012年第11期33卷 1393-1402页

作者：黄卫立蔡建乐 Department of Physics and Telecom Engineering Hunan City University College of Science Hangzhou Normal University

Conformal invariance and conserved quantities for a nonholonomic system of Chetaev＇s type with variable mass are studied. The conformal factor expressions are derived. The necessary and sufficient conditions are obtained to make the system＇s con- formal invariance Lie symmetrical. The conformal invariance of the weak and strong Lie symmetries for the system is given. The corresponding conserved quantities of the system are derived. Finally, an application of the result is shown with an example.

关键词： nonholonomic system variable mass conformal invariance conservedquantity

THE LIE SYMMETRIES AND CONSERVED QUANTITIES OF VARIABLE-MASS nonholonomic system OF NON-CHETAEV'S TYPE IN PHASE SPACE

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Applied Mathematics and Mechanics(English Edition) 2002年第10期23卷 1215-1220页

作者：方建会赵嵩卿焦志勇 Department of Applied Physics University of Petroleum Dongying 257061 Shandong P R China

The Lie symmetries and the conserved quantities of a variable mass nonholonomic system of non-Chetaev's type are studied by introducing the infinitesimal transformations of groups in phase space. By using the invariance of the differential equations of motion under the infinitesmal transformations of groups, the determining equations and the restriction equations of the Lie symmetries of the system are established, and the structure equations and the conserved quantities are obtained. An example is given to illustrate the application of the result.

关键词： nonholonomic system phase space analytic mechanics variable mass Lie symmetry conserved quantity

Unified Symmetry of nonholonomic system of Non-Chetaev＇s Type in Event Space

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Communications in Theoretical Physics 2007年第2期47卷 221-224页

作者： HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The unified symmetry of a nonholonomic system of non-Chetaev＇s type in event space under infinitesimal transformations of group is studied. Firstly, the differential equations of motion of the system are given. Secondly, the definition and the criterion of the unified symmetry for the system are obtained. Thirdly, a new conserved quantity, besides the Noether conserved quantity and the Hojman conserved quantity, is deduced from the unified symmetry of a nonholonomic system of non-Chetaev＇s type. Finally, an example is given to illustrate the application of the result.

关键词： event space nonholonomic system unified symmetry conserved quantity

Fractional Action-Like Variational Problem and Its Noether Symmetries for a nonholonomic system

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Transactions of Nanjing University of Aeronautics and Astronautics 2015年第4期32卷 380-389页

作者：张毅龙梓轩 College of Civil Engineering Suzhou University of Science and Technology College of Mathematics and Physics Suzhou University of Science and Technology

For an in-depth study on the symmetric properties for nonholonomic non-conservative mechanical systems,the fractional action-like Noether symmetries and conserved quantities for nonholonomic mechanical systems are studied,based on the fractional action-like approach for dynamics modeling proposed by ***,the fractional action-like variational problem is established,and the fractional action-like Lagrange equations of holonomic system and the fractional action-like differential equations of motion with multiplier for nonholonomic system are given;secondly,according to the invariance of fractional action-like Hamilton action under infinitesimal transformations of group,the definitions and criteria of fractional action-like Noether symmetric transformations and quasi-symmetric transformations are put forward;finally,the fractional action-like Noether theorems for both holonomic system and nonholonomic system are established,and the relationship between the fractional action-like Noether symmetry and the conserved quantity is given.

关键词： nonholonomic system fractional action-like variational problem symmetric transformation Noether theorem conserved quantity

THE CONSERVATION LAW OF nonholonomic system OF SECOND-ORDER NON-CHETAVE'S TYPE IN EVENT SPACE

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Applied Mathematics and Mechanics(English Edition) 2002年第1期23卷 89-94页

作者： FANG Jian-hui(方建会) Department of Applied Physics University of PetroleumDongying Shandong 257061 P R China

The conservation law of nonholonomic system of second-order non-Chataev's type in event space is studied The Jourdain's principle in event space is presented. The invariant condition of the Jourdain's principle under infinitesimal transformation is given by introducing Jourdain's generators in event space. Then the conservation law of the system in event space is obtained under certain conditions. Finally a calculating example is given.

关键词： event space Jourdain's principle nonholonomic system conservation law

Unified Symmetry of nonholonomic system of Non-Chetaev＇s Type with Variable Mass in Event Space

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Communications in Theoretical Physics 2007年第4X期48卷 619-622页

作者： HOU Qi-Bao LI Yuan-Cheng XiA Li-Li WANG Jing College of Physics Science and Technology China University of Petroleum Dongying 257061 China

The unified symmetry of a nonholonomic system of non-Chetaev＇s type with variable mass in event space is studied. The differential equations of motion of the system are given. Then the definition and the criterion of the unified symmetry for the system are obtained. Finally, the Noether conserved quantity, the Hojman conserved quantity, and a new type of conserved quantity are deduced from the unified symmetry of the nonholonomic system of non-Chetaev＇s type with variable mass in event space at one time. An example is given to illustrate the application of the results.

关键词： event space nonholonomic system variable mass unified symmetry conserved quantity

Exact Invariants and Adiabatic Invariants of Raitzin＇s Canonical Equations of Motion for nonholonomic system of Non-Chetaev＇s Type

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Communications in Theoretical Physics 2005年第6期43卷 987-992页

作者： QIAOYong-Fen ZHAOShu-Hong DepartmentofMechanicalEngineeringandAutomation ZhejiangSci-TchUniversityHangzhou310018China／／EngineeingCollegeofNortheastAgriculturalUniversityHarbin150030China

The exact invariants and the adiabatic invariants of Raitzin's canonical equations of motion for the nonholonomic system of non-Chetaev's type are studied. The relations between the invariants and the symmetries of the system are established. Based on the concept of higher order adiabatic invariant of mechanical system with the action of a small perturbation, the form of the exact invariants and adiabatic invariants and the conditions for their existence are proved. Finally, the inverse problem of the perturbation to symmetries of the system is studied and an example is also given to illustrate the application of the results.

关键词： nonholonomic system Raitzin's canonical equation symmetry perturbation exact invariant adiabatic invariant

Equivalence of Chetaev Model and Vacco Model in Ideal nonholonomic system and Active Realization Nonideal nonholonomic system

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Journal of Beijing Institute of Technology 2005年第1期14卷 109-112页

作者：赵跃宇金波许文喜 College of Civil Engineering Hunan University Changsha410082 China Department of Engineering Mechanics Hunan University Changsha410082 China Department

The Chetaev model and Vacco model in nonholonomic system are studied. The equivalence of the Chetaev model and Vacco model in ideal nonholonomic system and nonideal nonholonomic system realized actively is testified. If nonholonomic constraint is nonideal, the Vacco model is usable from the aspect of mathematics. A general method is given that can be utilized to deal with the ideal nonholonomic system and nonideal nonholonomic system realized actively.

关键词： nonholonomic system Chetaev definition Vacco dynamics equations of motion

Lie-Form Invariance of the nonholonomic system of Relative Motion in Event Space

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Communications in Theoretical Physics 2007年第5X期48卷 795-798页

作者： HOU Qi-Bao LI Yuan-Cheng WANG Jing XIA Li-Li College of Physics Science and Technology China University of Petroleum Dongying 257061 China

In this paper, the Lie-form invariance of a nonholonomic system of relative motion in event space is studied. Firstly, the definition and the criterion of the Lie-form invariance of the nonholonomic system of relative motion in event space is given. Secondly, the Hojman conserved quantity and a new type of conserved quantity deduced from the Lie-form invariance are obtained. An example is given to illustrate the application of the results.

关键词： event space nonholonomic system relative motion Lie-form invariance conserved quantity